Indoor vs outdoor is not really relevant to the discussion. Outdoor devices are waterproof and designed for wider temperatures. Otherwise there are similar designs for both indoor and outdoor.
If the antennas are the same 5DBi gain.both the antennas have the same wall penetrating powers as follows The input power is the same, the gain from the antenna is the same, the directionality is the same. Same amount of radiated energy from either one.
Most outdoor antennas ARE directional. There are omni outdoor antennas, but most of the time you are trying to connect to a signal from a specific location. Omni-directional outdoor access (to clients) is usually handled by outdoor access points rather than just antennas.
I think there are dual band antennas, because the wavelength of 5Ghz is approximately 1/2 the wavelength of 2.4Ghz. The antenna won't be equally efficient for the two frequencies, (say 3dBi on 2.4Ghz but 5dBi on 5Ghz).
Power solution:
power. that's all that matters. more power, more distance in FREE SPACE, or more PENETRATING power through WALLS. they are one and the same - the power is used to either carry the signal far with no obstacles, or just far enough through plenty of obstacles. power is all that matters.
outdoor stuff tends to be more ruggedly built, weatherproofed, etc.
2- You probably can, but to note, outdoor antennas are made for the varying weather outside.
For example, most outdoor antennas are made to point vertical with the top of the antenna facing upward. There usuailly a drain hole so that moisture can be release and doesn't fill up inside tha antenna. Outdoor antennas that mounted upside down usually need a small hole drilled on the top of the antenna to allow for moisture to escape.
So... you might be able to use it, but take into consideration the temperature and the moisture. If the antenna fails in a year or two, then you know to replace it with an outdoor antenna. Also, coax seal is good to cover up the connector so moisture doesn't ruin the cable and connectors. Also, make sure you have a drip loop on the cable so that moisture doesn't run into the connector or antenna housing.
3- It depends how much coverage area you required,because for example there will be more signal strength from a 7 dBI antenna than a 2.2dBI etc. Furthermore power level can be varied via controller.
check the following link for Power level.
http://www.cisco.com/c/en/us/support/docs/wireless-mobility/wireless-lan-wlan/23231-powervalues-23231.html